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Atomistic basis for continuum growth equation: Description of morphological evolution of GaAs during molecular beam epitaxy

机译：连续增长方程的原子基础：分子束外延过程中砷化镓形态演化的描述

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This review brings together experimental data on surface shape evolution during epitaxial growth of GaAs with kinetic Monte Carlo simulations of a solid-on-solid model and numerical solutions of a continuum growth equation derived from an adatom transport equation. Scanning probe and light scattering measurements of the surface morphology of GaAs, grown by molecular beam epitaxy, on planar as well as patterned (100) substrates are reviewed. We show that the experimental data can be described by a stable continuum growth equation that is mixed-order in the spatial derivatives, with an Edwards-Wilkinson type linear term, together with a conservative nonlinear term. The stable growth equation is derived from two coupled rate equations, one of which describes the transport of adatoms on the surface and the other describes the rate of change of surface height due to adatom incorporation into the surface at step edges. In this analysis, we assume that there is a combination of an Ehrlich-Schwoebel barrier and/or an incorporation barrier at step edges that favor a net downhill migration of adatoms across step edges, with the consequence that the growth model, like the experimental system, is stable, meaning that undulations in the surface tend to smooth out during growth. The coefficients in the growth equation depend on the growth rate and the density of steps on the surface. The continuum description of the morphological evolution is tested by conjparisons to computer experiments consisting of kinetic Monte Carlo simulations of a solid-on-solid model. The methods used in this analysis of GaAs epitaxy are expected to be broadly applicable to other materials that exhibit stable epitaxial growth.
机译：这篇综述汇集了有关GaAs外延生长过程中表面形状演变的实验数据，固体对固体模型的动力学蒙特卡洛模拟以及从原子迁移方程得出的连续生长方程的数值解。综述了分子束外延生长在平面以及图案化（100）衬底上的GaAs表面形态的扫描探针和光散射测量。我们表明，实验数据可以用一个稳定的连续增长方程来描述，该方程在空间导数中是混合阶的，与Edwards-Wilkinson型线性项以及保守的非线性项一起。稳定的增长方程式是从两个耦合的速率方程式导出的，其中一个描述了原子在表面上的迁移，另一个描述了由于原子在台阶边缘掺入表面而引起的表面高度变化率。在此分析中，我们假设台阶边缘存在Ehrlich-Schwoebel势垒和/或掺入势垒的组合，有利于跨阶跃边缘的吸附原子净下坡迁移，其结果是像实验系统一样，生长模型稳定，这意味着在生长过程中表面的起伏趋于平滑。生长方程中的系数取决于生长速率和表面台阶的密度。形态演变的连续描述是通过与计算机实验（包括固体对固体模型的动力学蒙特卡罗模拟）的对比来测试的。预期该GaAs外延分析中使用的方法将广泛应用于表现出稳定外延生长的其他材料。

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